Question

Consider this equation.sin(e)3/1010If 8 is an angle in quadrant Il, what is the value of tan(®)?

Answer 1

Given,

The equation is,

`sin\theta=(3√(10))/(10)`

Required

The value of tan theta.

The value of cos theta is,

`\begin{gathered} cos\theta=\sqrt{1-((3√(10))/(10)})^2 \\ =\sqrt{1-(90)/(100)} \\ =\sqrt{(10)/(100)} \\ =-(√(10))/(10) \end{gathered}`

The value of tan theta is,

`\begin{gathered} tan\theta=(sin\theta)/(cos\theta) \\ =(3√(10))/(10)*(-10)/(√(10)) \\ =-3 \end{gathered}`

Hence, the value of tan theta is -3.